Subgroups — C₇²×C₃⋊D₃×C₂₅ #36347778

Order 22050.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇²×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₇²×C₂₅	—	3	4	no	maximal
3	C₅×C₇²×C₃⋊D₃	C₅	1	1	yes	maximal, characteristic
4	C₃×C₇²×C₂₅	D₃	1	4	yes	complemented
5	C₇×C₃⋊D₃×C₂₅	C₇	1	8	yes	maximal, direct product factor
6	C₂×C₇²×C₂₅	—	9	1	no	Hall
7	C₃²×C₅×C₇²	C₂×C₅	1	1	yes	characteristic
8	C₃²×C₇×C₂₅	C₂×C₇	1	8	yes	complemented
9	C₅×D₃×C₇²	—	3	4	no	—
10	C₇²×C₂₅	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
11	D₃×C₇×C₂₅	—	3	32	no	—
12	C₇²×C₃⋊D₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅×C₇²	C₅×D₃	1	4	yes	—
14	C₅×C₇×C₃⋊D₃	C₅×C₇	1	8	yes	—
15	C₃×C₇×C₂₅	D₃×C₇	1	32	yes	complemented
16	C₂×C₅×C₇²	—	9	1	no	—
17	C₃⋊D₃×C₂₅	C₇²	1	1	yes	characteristic, direct product factor, Hall
18	C₃²×C₇²	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
19	C₂×C₇×C₂₅	—	9	8	no	—
20	C₃²×C₅×C₇	C₂×C₅×C₇	1	8	yes	—
21	D₃×C₇²	—	3	4	no	—
22	C₅×C₇²	C₅×C₃⋊D₃	1	1	yes	characteristic
23	C₃²×C₂₅	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
24	C₅×D₃×C₇	—	3	32	no	—
25	C₇×C₂₅	C₇×C₃⋊D₃	1	8	yes	direct product factor
26	D₃×C₂₅	—	3	4	no	—
27	C₃×C₇²	D₃×C₂₅	1	4	yes	complemented
28	C₇×C₃⋊D₃	C₇×C₂₅	1	8	yes	direct product factor
29	C₃×C₅×C₇	C₅×D₃×C₇	1	32	yes	—
30	C₂×C₇²	—	9	1	no	Hall
31	C₅×C₃⋊D₃	C₅×C₇²	1	1	yes	characteristic
32	C₃×C₂₅	D₃×C₇²	1	4	yes	complemented
33	C₂×C₅×C₇	—	9	8	no	—
34	C₃²×C₇	C₂×C₇×C₂₅	1	8	yes	complemented
35	C₂×C₂₅	—	9	1	no	Hall
36	C₇²	C₃⋊D₃×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
37	C₃²×C₅	C₂×C₅×C₇²	1	1	yes	characteristic
38	D₃×C₇	—	3	32	no	—
39	C₅×C₇	C₅×C₇×C₃⋊D₃	1	8	yes	—
40	C₅×D₃	—	3	4	no	—
41	C₂₅	C₇²×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
42	C₃×C₇	D₃×C₇×C₂₅	1	32	yes	complemented
43	C₃⋊D₃	C₇²×C₂₅	1	1	yes	characteristic, direct product factor, Hall
44	C₃×C₅	C₅×D₃×C₇²	1	4	yes	—
45	C₂×C₇	—	9	8	no	—
46	C₂×C₅	—	9	1	no	—
47	C₃²	C₂×C₇²×C₂₅	1	1	yes	characteristic, complemented, Sylow
48	C₇	C₇×C₃⋊D₃×C₂₅	1	8	yes	direct product factor
49	D₃	—	3	4	no	—
50	C₅	C₅×C₇²×C₃⋊D₃	1	1	yes	characteristic
51	C₃	D₃×C₇²×C₂₅	1	4	yes	complemented
52	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇²×C₂₅	C₃⋊D₃
commutator, hypocenter	C₃²	C₂×C₇²×C₂₅
Frattini	C₅	C₅×C₇²×C₃⋊D₃
Fitting	C₃²×C₇²×C₂₅	C₂
socle	C₃²×C₅×C₇²	C₂×C₅
prime radical	C₅×C₇²×C₃⋊D₃	C₅
cosocle	C₃²×C₅	C₂×C₅×C₇²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₇²×C₂₅

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃²×C₇²×C₂₅	C₂	semidirect
4. C₃×C₇²×C₂₅	D₃	semidirect
5. C₇×C₃⋊D₃×C₂₅	C₇	direct (N × H)
8. C₃²×C₇×C₂₅	C₂×C₇	semidirect
10. C₇²×C₂₅	C₃⋊D₃	direct (N × H)
12. C₇²×C₃⋊D₃	C₂₅	direct (N × H)
15. C₃×C₇×C₂₅	D₃×C₇	semidirect
17. C₃⋊D₃×C₂₅	C₇²	direct (N × H)
18. C₃²×C₇²	C₂×C₂₅	semidirect
23. C₃²×C₂₅	C₂×C₇²	semidirect
25. C₇×C₂₅	C₇×C₃⋊D₃	direct (N × H)
27. C₃×C₇²	D₃×C₂₅	semidirect
28. C₇×C₃⋊D₃	C₇×C₂₅	direct (N × H)
32. C₃×C₂₅	D₃×C₇²	semidirect
34. C₃²×C₇	C₂×C₇×C₂₅	semidirect
36. C₇²	C₃⋊D₃×C₂₅	direct (N × H)
41. C₂₅	C₇²×C₃⋊D₃	direct (N × H)
42. C₃×C₇	D₃×C₇×C₂₅	semidirect
43. C₃⋊D₃	C₇²×C₂₅	direct (N × H)
47. C₃²	C₂×C₇²×C₂₅	semidirect
48. C₇	C₇×C₃⋊D₃×C₂₅	direct (N × H)
51. C₃	D₃×C₇²×C₂₅	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₇²×C₂₅	2
D₃×C₇²×C₂₅	3
C₅×C₇²×C₃⋊D₃	5
C₇×C₃⋊D₃×C₂₅	7

Subgroups — C72×C3⋊D3×C25 #36347778

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇²×C₃⋊D₃×C₂₅ #36347778